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The phrase "a complicated form" is correct and usable in written English.
It can be used to describe a structure, document, or concept that has many intricate or complex elements.
Example: "The application requires a complicated form that includes multiple sections and detailed information."
Alternatives: "a complex structure" or "a convoluted format".
Exact(22)
Judge Wilson seemed skeptical of how Elian could have understood a complicated form requesting an asylum hearing.
Or he can ask Wirral council to top up his rent, by filling out a complicated form that asks for proof of his weekly spend on everything from cigarettes to toiletries.
They usually take a complicated form, but if one imagines contours drawn at very close intervals of height and a small portion of the map to be greatly enlarged, the contours of this local region will become very nearly straight, like the two drawn in Figure 6 for heights h and h + δh.
The cost function in (60) has a complicated form with respect to the unknown parameters.
The impact of a wind turbine and a boat takes a complicated form.
From (6) and (7), it is seen that (10) is related to W i and D j in a complicated form.
Similar(36)
Zhang used a very complicated form of a simple device for finding primes called a sieve, invented by a Greek named Eratosthenes, a contemporary of Archimedes.
Because the fractional derivative of a compound function has a very complicated form, most of the current observers which were designed for classical nonlinear systems cannot be used to fractional ones directly.
This is a slightly complicated form of nonsense.
The Obama administration is moving to simplify the Free Application for Federal Student Aid, or Fafsa, a notoriously complicated form that asks students seeking financial aid for college as many as 153 questions.
However, the controller in [30] has a very complicated form.
More suggestions(17)
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com